Bottom Line:
Enzymatic activities of the two modeled ribozymes are in trade-off with their replication rates, and the relative replication rates compared to those of complementary strands are evolvable traits of the ribozymes.Although some asymmetry between gene and enzymatic strands could have evolved even in earlier, surface-bound systems, the shown mechanism in protocells seems inevitable and under strong positive selection.This could have preadapted the genetic system for transcription after the subsequent origin of chromosomes and DNA.

ABSTRACTThe RNA world is a very likely interim stage of the evolution after the first replicators and before the advent of the genetic code and translated proteins. Ribozymes are known to be able to catalyze many reaction types, including cofactor-aided metabolic transformations. In a metabolically complex RNA world, early division of labor between genes and enzymes could have evolved, where the ribozymes would have been transcribed from the genes more often than the other way round, benefiting the encapsulating cells through this dosage effect. Here we show, by computer simulations of protocells harboring unlinked RNA replicators, that the origin of replicational asymmetry producing more ribozymes from a gene template than gene strands from a ribozyme template is feasible and robust. Enzymatic activities of the two modeled ribozymes are in trade-off with their replication rates, and the relative replication rates compared to those of complementary strands are evolvable traits of the ribozymes. The degree of trade-off is shown to have the strongest effect in favor of the division of labor. Although some asymmetry between gene and enzymatic strands could have evolved even in earlier, surface-bound systems, the shown mechanism in protocells seems inevitable and under strong positive selection. This could have preadapted the genetic system for transcription after the subsequent origin of chromosomes and DNA.

pcbi-1003936-g004: Factors affecting the rate of asymmetry between the minus and the plus strands.(A) In cases when the strength of trade-off is high (), the asymmetry between the minus and plus strands is strong, however as the strength of trade-off decreases (), since in these cases molecules can achieve high metabolic activity without trading off their replication affinities, the asymmetry becomes less pronounced. (B) As the number of the initial number of molecules () per vesicle is increased () the rate of asymmetry gradually decreases (). (C) The effect of kinetic parameters for strong trade-off (blue lines: ) and for weak trade-off (green lines: ). Here we increased the inflow rate of source material from the environment into the vesicle () (light blue and green lines: and ; middle dark blue and green lines: and ; dark blue and green lines: and ). For low inflow rate and kinetic constants, high metabolic activities of minus strands evolve, which results in high rate of asymmetries between the two strands. However lowering the inflow rate or the kinetic rate of reactions beyond a threshold results in the extinction of replicators (notice the absence of equilibrium ratio of asymmetry, for example , and , i.e. left hand side of the light blue curve). The results are averaged over 5 replicate model runs, and over 1,000,000 molecular update steps after reaching equilibrium. Whiskered bars represent the standard errors of the replicate runs. Other parameters (if not stated otherwise): , , , , , , , , , , , and .

Mentions:
Average copy number of plus strands can be reduced through evolution even to 1 or 2 gene strands per protocell in cases when trade-off is strong between replication and enzymatic rates. The survival of plus strands in such cases is ensured by the fact that they can be copied from the ribozymes. Figure 2 shows an example of such a successful division of labor between enzymes and genes. In Figure 3 we demonstrate that evolutionary trajectories converge to the same equilibrium ratio of division of labor from different initial states, even when the evolution of replication rates and enzymatic rates is not bound, but only limited by the trade-off function assumed, and when the replication affinity of the plus strand is also allowed to evolve (Figure 3). Less pronounced division of labor is observed for weaker trade-off between replication rate and metabolic efficiency (Figure 4A), for higher numbers of molecules per protocell (Figure 4B), and for higher food concentration and kinetic rate constants (Figure 4C). By far the strongest effect is that of the trade-off, which is understandable, since it is a trait that affects every ribozyme individually. The mild decrease with protocell size is due to the fact that if there are many RNA molecules in total, there are likely to be many enzymes present anyhow, thus the force of selection should decline with protocell size. Similarly, higher food concentrations and higher kinetic rate constants reduce the force of selection for very high enzymatic efficiency. We note that some division of labor evolves even with negligible trade-off: this we attribute to the metabolic cost of the templates. In short, for the same total template copy number, protocells harboring more enzymes than genes are better off than those with reversed proportions, since the former carry a smaller load of “useless” templates (redundant genes). This effect becomes more pronounced with low food concentrations and kinetic rate constants, as in these cases the selective advantage of protocells with more enzymes increases (Figure 4C). Of course, assortment load (i.e., the drop in average fitness due to the random loss of any essential gene after stochastic assortment of templates in the two daughter protocells), and the fact that high enzymatic efficiency can already be reached without evolving high rate of strand asymmetry, prevents the system from evolving stronger asymmetry without strong trade-off.

pcbi-1003936-g004: Factors affecting the rate of asymmetry between the minus and the plus strands.(A) In cases when the strength of trade-off is high (), the asymmetry between the minus and plus strands is strong, however as the strength of trade-off decreases (), since in these cases molecules can achieve high metabolic activity without trading off their replication affinities, the asymmetry becomes less pronounced. (B) As the number of the initial number of molecules () per vesicle is increased () the rate of asymmetry gradually decreases (). (C) The effect of kinetic parameters for strong trade-off (blue lines: ) and for weak trade-off (green lines: ). Here we increased the inflow rate of source material from the environment into the vesicle () (light blue and green lines: and ; middle dark blue and green lines: and ; dark blue and green lines: and ). For low inflow rate and kinetic constants, high metabolic activities of minus strands evolve, which results in high rate of asymmetries between the two strands. However lowering the inflow rate or the kinetic rate of reactions beyond a threshold results in the extinction of replicators (notice the absence of equilibrium ratio of asymmetry, for example , and , i.e. left hand side of the light blue curve). The results are averaged over 5 replicate model runs, and over 1,000,000 molecular update steps after reaching equilibrium. Whiskered bars represent the standard errors of the replicate runs. Other parameters (if not stated otherwise): , , , , , , , , , , , and .

Mentions:
Average copy number of plus strands can be reduced through evolution even to 1 or 2 gene strands per protocell in cases when trade-off is strong between replication and enzymatic rates. The survival of plus strands in such cases is ensured by the fact that they can be copied from the ribozymes. Figure 2 shows an example of such a successful division of labor between enzymes and genes. In Figure 3 we demonstrate that evolutionary trajectories converge to the same equilibrium ratio of division of labor from different initial states, even when the evolution of replication rates and enzymatic rates is not bound, but only limited by the trade-off function assumed, and when the replication affinity of the plus strand is also allowed to evolve (Figure 3). Less pronounced division of labor is observed for weaker trade-off between replication rate and metabolic efficiency (Figure 4A), for higher numbers of molecules per protocell (Figure 4B), and for higher food concentration and kinetic rate constants (Figure 4C). By far the strongest effect is that of the trade-off, which is understandable, since it is a trait that affects every ribozyme individually. The mild decrease with protocell size is due to the fact that if there are many RNA molecules in total, there are likely to be many enzymes present anyhow, thus the force of selection should decline with protocell size. Similarly, higher food concentrations and higher kinetic rate constants reduce the force of selection for very high enzymatic efficiency. We note that some division of labor evolves even with negligible trade-off: this we attribute to the metabolic cost of the templates. In short, for the same total template copy number, protocells harboring more enzymes than genes are better off than those with reversed proportions, since the former carry a smaller load of “useless” templates (redundant genes). This effect becomes more pronounced with low food concentrations and kinetic rate constants, as in these cases the selective advantage of protocells with more enzymes increases (Figure 4C). Of course, assortment load (i.e., the drop in average fitness due to the random loss of any essential gene after stochastic assortment of templates in the two daughter protocells), and the fact that high enzymatic efficiency can already be reached without evolving high rate of strand asymmetry, prevents the system from evolving stronger asymmetry without strong trade-off.

Bottom Line:
Enzymatic activities of the two modeled ribozymes are in trade-off with their replication rates, and the relative replication rates compared to those of complementary strands are evolvable traits of the ribozymes.Although some asymmetry between gene and enzymatic strands could have evolved even in earlier, surface-bound systems, the shown mechanism in protocells seems inevitable and under strong positive selection.This could have preadapted the genetic system for transcription after the subsequent origin of chromosomes and DNA.

ABSTRACTThe RNA world is a very likely interim stage of the evolution after the first replicators and before the advent of the genetic code and translated proteins. Ribozymes are known to be able to catalyze many reaction types, including cofactor-aided metabolic transformations. In a metabolically complex RNA world, early division of labor between genes and enzymes could have evolved, where the ribozymes would have been transcribed from the genes more often than the other way round, benefiting the encapsulating cells through this dosage effect. Here we show, by computer simulations of protocells harboring unlinked RNA replicators, that the origin of replicational asymmetry producing more ribozymes from a gene template than gene strands from a ribozyme template is feasible and robust. Enzymatic activities of the two modeled ribozymes are in trade-off with their replication rates, and the relative replication rates compared to those of complementary strands are evolvable traits of the ribozymes. The degree of trade-off is shown to have the strongest effect in favor of the division of labor. Although some asymmetry between gene and enzymatic strands could have evolved even in earlier, surface-bound systems, the shown mechanism in protocells seems inevitable and under strong positive selection. This could have preadapted the genetic system for transcription after the subsequent origin of chromosomes and DNA.